# 拓撲連續映射基礎 · 脈衝 R03

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261013-advance-20261019-r03-topological-continuity-foundations · 2026-10-13 · 100 題



## 1. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,2,3],"target_open":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [], [], 是)

第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0001/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 2. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"images":[1,0,2,3],"target_open":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1], [0], 否)

第二批擴展核對=(4, 4, [1], [0], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0002/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 3. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,1,3],"target_open":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1], [2], 是)

第二批擴展核對=(4, 4, [1], [2], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0003/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 4. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"images":[3,0,1,2],"target_open":[0,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [0, 2, 3], [0, 1, 3], 是)

第二批擴展核對=(4, 4, [0, 2, 3], [0, 1, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0004/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 5. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,1,3],"target_open":[2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [2], [1], 否)

第二批擴展核對=(4, 4, [2], [1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0005/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 6. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"images":[1,2,0,3],"target_open":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [], [], 是)

第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0006/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 7. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,0,3],"target_open":[1,2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1, 2], [0, 1], 否)

第二批擴展核對=(4, 4, [1, 2], [0, 1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0007/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 8. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"images":[3,1,0,2],"target_open":[2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [2, 3], [0, 3], 否)

第二批擴展核對=(4, 4, [2, 3], [0, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0008/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 9. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,1,2],"target_open":[3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [3], [1], 否)

第二批擴展核對=(4, 4, [3], [1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0009/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 10. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"images":[1,3,0,2],"target_open":[0,1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)

第二批擴展核對=(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0010/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 11. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,0,1],"target_open":[1,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1, 3], [1, 3], 否)

第二批擴展核對=(4, 4, [1, 3], [1, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0011/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 12. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"images":[3,2,0,1],"target_open":[3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [3], [0], 否)

第二批擴展核對=(4, 4, [3], [0], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0012/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 13. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,3,2],"target_open":[2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [2, 3], [2, 3], 否)

第二批擴展核對=(4, 4, [2, 3], [2, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0013/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 14. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"images":[1,0,3,2],"target_open":[1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1, 2, 3], [0, 2, 3], 否)

第二批擴展核對=(4, 4, [1, 2, 3], [0, 2, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0014/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 15. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,3,1],"target_open":[1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1, 2, 3], [0, 2, 3], 是)

第二批擴展核對=(4, 4, [1, 2, 3], [0, 2, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0015/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 16. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"images":[3,0,2,1],"target_open":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [], [], 是)

第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0016/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 17. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,3,1],"target_open":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [], [], 是)

第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0017/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 18. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"images":[1,2,3,0],"target_open":[0,1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [0, 1], [0, 3], 否)

第二批擴展核對=(4, 4, [0, 1], [0, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0018/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 19. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,3,0],"target_open":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1], [1], 否)

第二批擴展核對=(4, 4, [1], [1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0019/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 20. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"images":[3,1,2,0],"target_open":[0,1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)

第二批擴展核對=(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0020/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 21. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,2,1],"target_open":[2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [2], [2], 否)

第二批擴展核對=(4, 4, [2], [2], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0021/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 22. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"images":[1,3,2,0],"target_open":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1], [0], 否)

第二批擴展核對=(4, 4, [1], [0], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0022/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 23. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,1,0],"target_open":[1,2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1, 2], [0, 2], 否)

第二批擴展核對=(4, 4, [1, 2], [0, 2], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0023/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 24. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":4,"m":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"images":[3,2,1,0],"target_open":[1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(4, 4, [1, 2, 3], [0, 1, 2], 否)

第二批擴展核對=(4, 4, [1, 2, 3], [0, 1, 2], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0024/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 25. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-single-preimage；資料={"n":3,"m":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"images":[0,1,2],"target_open":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。

查看答案與解釋(3, 3, [], [], 是)

第二批擴展核對=(3, 3, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0025/)

拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate





## 26. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,2,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([0, 1, 2, 3], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0026/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 27. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"images":[1,0,2,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([1, 0, 2, 3], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([1, 0, 2, 3], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0027/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 28. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,1,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([2, 0, 1, 3], [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([2, 0, 1, 3], [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0028/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 29. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"images":[3,0,1,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([3, 0, 1, 2], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([3, 0, 1, 2], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0029/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 30. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,1,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 2, 1, 3], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([0, 2, 1, 3], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0030/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 31. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"images":[1,2,0,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([1, 2, 0, 3], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([1, 2, 0, 3], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0031/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 32. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,0,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([2, 1, 0, 3], [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([2, 1, 0, 3], [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0032/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 33. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"images":[3,1,0,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([3, 1, 0, 2], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([3, 1, 0, 2], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0033/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 34. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,1,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 3, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([0, 3, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0034/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 35. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"images":[1,3,0,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([1, 3, 0, 2], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([1, 3, 0, 2], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0035/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 36. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,0,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([2, 3, 0, 1], [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([2, 3, 0, 1], [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0036/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 37. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"images":[3,2,0,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([3, 2, 0, 1], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([3, 2, 0, 1], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0037/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 38. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,3,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 1, 3, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([0, 1, 3, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0038/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 39. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"images":[1,0,3,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([1, 0, 3, 2], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([1, 0, 3, 2], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0039/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 40. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,3,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([2, 0, 3, 1], [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([2, 0, 3, 1], [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0040/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 41. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"images":[3,0,2,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([3, 0, 2, 1], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([3, 0, 2, 1], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0041/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 42. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,3,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 2, 3, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([0, 2, 3, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0042/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 43. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"images":[1,2,3,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([1, 2, 3, 0], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([1, 2, 3, 0], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0043/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 44. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,3,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([2, 1, 3, 0], [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([2, 1, 3, 0], [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0044/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 45. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"images":[3,1,2,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([3, 1, 2, 0], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([3, 1, 2, 0], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0045/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 46. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,2,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 3, 2, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([0, 3, 2, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0046/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 47. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"images":[1,3,2,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([1, 3, 2, 0], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([1, 3, 2, 0], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0047/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 48. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,1,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([2, 3, 1, 0], [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([2, 3, 1, 0], [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0048/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 49. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":4,"m":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"images":[3,2,1,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([3, 2, 1, 0], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)

第二批擴展核對=([3, 2, 1, 0], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0049/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 50. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-full-audit；資料={"n":3,"m":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"images":[0,1,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。

查看答案與解釋([0, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], 否)

第二批擴展核對=([0, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0050/)

拓撲連續映射 · qf-ext19-continuity-full-audit · candidate





## 51. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,1,2,3],"images_g":[0,1,2,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0051/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 52. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,0,2,3],"images_g":[3,1,0,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([1, 0, 2, 3], [3, 1, 0, 2], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([1, 0, 2, 3], [3, 1, 0, 2], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0052/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 53. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,0,1,3],"images_g":[2,0,3,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([2, 0, 1, 3], [2, 0, 3, 1], [3, 2, 0, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([2, 0, 1, 3], [2, 0, 3, 1], [3, 2, 0, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0053/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 54. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,0,1,2],"images_g":[1,3,2,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([3, 0, 1, 2], [1, 3, 2, 0], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([3, 0, 1, 2], [1, 3, 2, 0], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0054/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 55. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,2,1,3],"images_g":[0,2,1,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 2, 1, 3], [0, 2, 1, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([0, 2, 1, 3], [0, 2, 1, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0055/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 56. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,2,0,3],"images_g":[3,2,0,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([1, 2, 0, 3], [3, 2, 0, 1], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([1, 2, 0, 3], [3, 2, 0, 1], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0056/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 57. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,1,0,3],"images_g":[2,1,3,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([2, 1, 0, 3], [2, 1, 3, 0], [3, 1, 2, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([2, 1, 0, 3], [2, 1, 3, 0], [3, 1, 2, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0057/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 58. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,1,0,2],"images_g":[1,0,2,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([3, 1, 0, 2], [1, 0, 2, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([3, 1, 0, 2], [1, 0, 2, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0058/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 59. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,3,1,2],"images_g":[0,3,1,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 3, 1, 2], [0, 3, 1, 2], [0, 2, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([0, 3, 1, 2], [0, 3, 1, 2], [0, 2, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0059/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 60. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,3,0,2],"images_g":[3,0,2,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([1, 3, 0, 2], [3, 0, 2, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([1, 3, 0, 2], [3, 0, 2, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0060/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 61. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,3,0,1],"images_g":[2,3,1,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([2, 3, 0, 1], [2, 3, 1, 0], [1, 0, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([2, 3, 0, 1], [2, 3, 1, 0], [1, 0, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0061/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 62. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,2,0,1],"images_g":[1,2,0,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([3, 2, 0, 1], [1, 2, 0, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([3, 2, 0, 1], [1, 2, 0, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0062/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 63. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,1,3,2],"images_g":[0,1,3,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 1, 3, 2], [0, 1, 3, 2], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([0, 1, 3, 2], [0, 1, 3, 2], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0063/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 64. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,0,3,2],"images_g":[3,1,2,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([1, 0, 3, 2], [3, 1, 2, 0], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([1, 0, 3, 2], [3, 1, 2, 0], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0064/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 65. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,0,3,1],"images_g":[2,0,1,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([2, 0, 3, 1], [2, 0, 1, 3], [1, 2, 3, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([2, 0, 3, 1], [2, 0, 1, 3], [1, 2, 3, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0065/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 66. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,0,2,1],"images_g":[1,3,0,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([3, 0, 2, 1], [1, 3, 0, 2], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([3, 0, 2, 1], [1, 3, 0, 2], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0066/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 67. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,2,3,1],"images_g":[0,2,3,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 2, 3, 1], [0, 2, 3, 1], [0, 3, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([0, 2, 3, 1], [0, 2, 3, 1], [0, 3, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0067/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 68. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,2,3,0],"images_g":[3,2,1,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([1, 2, 3, 0], [3, 2, 1, 0], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([1, 2, 3, 0], [3, 2, 1, 0], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0068/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 69. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,1,3,0],"images_g":[2,1,0,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([2, 1, 3, 0], [2, 1, 0, 3], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([2, 1, 3, 0], [2, 1, 0, 3], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0069/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 70. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,1,2,0],"images_g":[1,0,3,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([3, 1, 2, 0], [1, 0, 3, 2], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([3, 1, 2, 0], [1, 0, 3, 2], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0070/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 71. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,3,2,1],"images_g":[0,3,2,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 3, 2, 1], [0, 3, 2, 1], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([0, 3, 2, 1], [0, 3, 2, 1], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0071/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 72. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,3,2,0],"images_g":[3,0,1,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([1, 3, 2, 0], [3, 0, 1, 2], [0, 2, 1, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([1, 3, 2, 0], [3, 0, 1, 2], [0, 2, 1, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0072/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 73. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,3,1,0],"images_g":[2,3,0,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([2, 3, 1, 0], [2, 3, 0, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([2, 3, 1, 0], [2, 3, 0, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0073/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 74. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":4,"m":4,"k":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,2,1,0],"images_g":[1,2,3,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([3, 2, 1, 0], [1, 2, 3, 0], [0, 3, 2, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])

第二批擴展核對=([3, 2, 1, 0], [1, 2, 3, 0], [0, 3, 2, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0074/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 75. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-composition；資料={"n":3,"m":3,"k":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"opens_z":[[],[0,1,2]],"images_f":[0,1,2],"images_g":[0,1,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。

查看答案與解釋([0, 1, 2], [0, 1, 2], [0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2], [0, 1, 2], 是]])

第二批擴展核對=([0, 1, 2], [0, 1, 2], [0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2], [0, 1, 2], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0075/)

拓撲連續映射 · qf-ext19-continuity-composition · candidate





## 76. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,2,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 1, 2, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([0, 1, 2, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0076/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 77. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"images":[1,0,2,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([1, 0, 2, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([1, 0, 2, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0077/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 78. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,1,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([2, 0, 1, 3], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[0, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([2, 0, 1, 3], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[0, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0078/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 79. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"images":[3,0,1,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([3, 0, 1, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[0, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([3, 0, 1, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[0, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0079/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 80. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,1,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 2, 1, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([0, 2, 1, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0080/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 81. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"images":[1,2,0,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([1, 2, 0, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([1, 2, 0, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0081/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 82. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,0,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([2, 1, 0, 3], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([2, 1, 0, 3], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0082/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 83. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"images":[3,1,0,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([3, 1, 0, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([3, 1, 0, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0083/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 84. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,1,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 3, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 2], 是], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([0, 3, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 2], 是], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0084/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 85. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"images":[1,3,0,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([1, 3, 0, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([1, 3, 0, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0085/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 86. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,0,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([2, 3, 0, 1], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([2, 3, 0, 1], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0086/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 87. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"images":[3,2,0,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([3, 2, 0, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([3, 2, 0, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0087/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 88. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,3,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 1, 3, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([0, 1, 3, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0088/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 89. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"images":[1,0,3,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([1, 0, 3, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([1, 0, 3, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0089/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 90. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,3,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([2, 0, 3, 1], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[0, 2], [2, 3], 是], [[0, 2, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([2, 0, 3, 1], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[0, 2], [2, 3], 是], [[0, 2, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0090/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 91. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"images":[3,0,2,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([3, 0, 2, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[0, 3], [1, 3], 否], [[0, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([3, 0, 2, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[0, 3], [1, 3], 否], [[0, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0091/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 92. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,3,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 2, 3, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 3], 是], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([0, 2, 3, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 3], 是], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0092/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 93. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"images":[1,2,3,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([1, 2, 3, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [2, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([1, 2, 3, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [2, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0093/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 94. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,3,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([2, 1, 3, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[1, 2], [1, 3], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([2, 1, 3, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[1, 2], [1, 3], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0094/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 95. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"images":[3,1,2,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([3, 1, 2, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([3, 1, 2, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0095/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 96. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,2,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 3, 2, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([0, 3, 2, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0096/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 97. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"images":[1,3,2,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([1, 3, 2, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([1, 3, 2, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0097/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 98. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,1,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([2, 3, 1, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[2, 3], [0, 1], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)

第二批擴展核對=([2, 3, 1, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[2, 3], [0, 1], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0098/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 99. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":4,"m":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"images":[3,2,1,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([3, 2, 1, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)

第二批擴展核對=([3, 2, 1, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0099/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate





## 100. 有限拓撲連續性

完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={"n":3,"m":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"images":[0,1,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。

查看答案與解釋([0, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是]], 性質不同)

第二批擴展核對=([0, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r03-topological-continuity-0100/)

拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261019-r03-topological-continuity-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261019-r03-topological-continuity-foundations/validation-report.json)